Apparently, the resolution of the debt ceiling restored the dollar's status as a safe haven in the eyes of the world's investors. That accelerated the flight from European sovereign debt and European banks. That in turn raised fears in financial markets, driving down stocks, including in the United States.
I think one can make a plausible argument that we would be better off continuing debt ceiling games in the US. It looks as if certain European countries -- the usual suspects of Italy, Greece, and Spain among them -- face self-fulfilling beliefs regarding the quality of their debt. They can survive only if investors continue to lend to them at low rates. There are multiple equilibria here -- either peripheral countries continue to borrow at cheap rates reflecting a low probability of default, or they borrow at high rates reflecting a high probability of default.
Which equilibria we are in is determined by the initial level of capital willing to invest in Europe versus America. As Kling points out, the resolution of "uncertainty" in the US shifted the balance in favor of the US, pushing Europe to the bad equilibrium, with internationally disastrous consequences. Of course, keeping America a risky destination for capital probably isn't the best long-term strategy. But perhaps a more stringent regime of capital flows could have alleviated some of the short-run European liquidity problems, buying time to deal with the solvency concerns.
Elsewhere, Ryan Avent offers a useful historical perspective comparing today with the 1930s. It is a useful analogy, one that largely fits the narrative I got from the excellent Wages of Destruction. The euro, in this reading, in some sense serves the same function as the Gold Standard did for European countries -- a straightjacket preventing adequate monetary easing in poorly functioning economies, who have contracted out the ability to ease and do not receive fiscal transfers from elsewhere.